Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 11 - Counting Methods and Probability Theory - 11.3 Combinations - Exercise Set 11.3: 36

Answer

$45,057,474$ selections

Work Step by Step

A combination from a group of items occurs when no item is used more than once and the order of items makes no difference. The number of combinations possible if $r$ items are taken from $n$ items is ${}_{n}C_{r}=\displaystyle \frac{n!}{(n-r)!r!}$ -------------- Order is not important, we deal with combinations. ${}_{59}C_{6}=\displaystyle \frac{59!}{(59-6)!6!}$ $=\displaystyle \frac{59\times 58\times 57\times 56\times 55\times 54}{1\times 2\times 3\times 4\times 5\times 6}$ $=\displaystyle \frac{59\times 58\times 57\times 7\times 11\times 3}{1\times 1\times 1\times 1\times 1\times 1}$ $=45,057,474$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.